Question

mrs. perez has been asked to place 1.5, -2.85, π, $\frac{11}{6}$, -1.5, $sqrt{9}$ on the number line.

explain the process for the placement of the numbers on the number line.

Explanation:

Step1: Convert all to decimals

$1.5 = 1.5$, $-2.85 = -2.85$, $\pi \approx 3.14$, $\frac{11}{6} \approx 1.83$, $-1.5 = -1.5$, $\sqrt{9}=3$

Step2: Order from smallest to largest

$-2.85 < -1.5 < 1.5 < 1.83 < 3 < 3.14$

Step3: Match to number line

Align ordered values with positions between -3 and 3:

• $-2.85$ (close to -3), $-1.5$ (midway -3 and 0), $1.5$ (midway 0 and 3), $\frac{11}{6}\approx1.83$ (right of 1.5), $\sqrt{9}=3$ (at 3), $\pi\approx3.14$ (just right of 3)

Answer:

1. First, convert all numbers to decimal form for easy comparison:

• $1.5$ remains $1.5$
• $-2.85$ remains $-2.85$
• $\pi \approx 3.14$
• $\frac{11}{6} \approx 1.83$
• $-1.5$ remains $-1.5$
• $\sqrt{9} = 3$

1. Order the decimals from smallest to largest:

$-2.85 < -1.5 < 1.5 < \frac{11}{6} < \sqrt{9} < \pi$

1. Place each number on the number line:

• Mark $-2.85$ just to the right of $-3$
• Mark $-1.5$ halfway between $-3$ and $0$
• Mark $1.5$ halfway between $0$ and $3$
• Mark $\frac{11}{6}\approx1.83$ just to the right of $1.5$
• Mark $\sqrt{9}=3$ exactly at the labeled $3$
• Mark $\pi\approx3.14$ just to the right of $3$